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Truncation of LSB's

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Posted on June 3, 2017 at 10:24:52
sideliner
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  Since: December 15, 2023
 This is for the experts in digital conversion: in the Stereophile review of the Schiit Yggdrasil, JA asserts that because the DAC chip used is a 20 bit device, for 24-bit audio it must truncate the LSB's which is a process that causes distortion. I understand that not all opinions are in agreement on this, or even perhaps to what degree it matters to those that believe in the negative audible effects of LSB truncation.

However, if we were to assume that this distortion does have audible effects, I'm just curious to know of the possible ways to have DAC's of 20 or even 16 bits accept 24-bit audio without throwing out bits. Isn't there a way to use multiple chips in parallel to accomplish this? If so, how many 20-bit chips would be needed to process 24-bit audio? How about using a 20 bit DAC for say the first 20 bits (MSB's) and a discreet resistor R-2R DAC to handle the 4 LSB's? Is something like that even possible?

 

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RE: Truncation of LSB's, posted on June 3, 2017 at 14:04:54
knewton
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 Your seemingly simple questions have some complex answers. There are two well known ways to feed a data stream featuring a given bit-depth to a D/A unit featuring some lesser native bit-depth. The first way is to dither the incoming data to the lesser bit-depth rather than simply truncating it. This will remove the distortion of truncation at the price of increasing the channel noise floor. The other way is via sigma-delta-modulation(SDM), which can deliver the full dynamic range of the higher resolution original data, but only within a limited band. This is what most commercial D/A chips do, even when fed only 16-bits. These D/A chips typically feature only a 5-bit or 6-bit core, and utilize SDM to deliver the full resolution (SNR) of the original higher resolution data, within practical circuit limits, of course.

As far as various hybrid converter topologies are concerned, most of these have been tried over the years. The currently in production PCM1794A DAC chip is based on a hybrid converter core, while also utilizing SDM. The out of production PCM1704 R-2R DAC chip is actually a hybrid of two internal 23-bit R-2R cores coordinated to function as a single 24-bit complex converter. An architecture Burr-Brown refered to as 'colinear' in the data sheet. As a rule of thumb with the complex merging of multiple converter cores, each extra bit of resolution requires a doubling of converter circuitry. Simply paralleling converter outputs does not increase bit resolution. It only reduces the random noise floor by 3dB for every doubling of the number of converters.

High resolution discrete R-2R converters that reliably retain high accuracy are non-trivial to design and consistently manufacture. Such converters are, however, becoming in vogue among DAC vendors seeking to differentiate themselves in a crowded market. However, none of these which I'm aware objectively match the consistent accuracy of today's top multi-bit SDM converter chips. Subjective assessments may, and do, differ of course.
_
Ken Newton

 

Thanks for that explanation. nt, posted on June 3, 2017 at 15:43:32
jusbe
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Big J

"... only a very few individuals understand as yet that personal salvation is a contradiction in terms."


 

+1 (nt), posted on June 3, 2017 at 18:15:16
Charles Hansen
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 nt

 

RE: Truncation of LSB's, posted on June 4, 2017 at 00:34:49
Frihed89
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 "High resolution discrete R-2R converters that reliably retain high accuracy are non-trivial to design and consistently manufacture".

This also seems to be the case for 44.1/16 R-2R Dacs. Audio Note (UK) has been working on one for a few years, but it seems stalled due to these issues.

 

Precision, posted on June 4, 2017 at 01:50:18
jusbe
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 Last I heard, it was an issue of reliably and consistently being able to produce resistors to the required precision for each DAC - at a reasonable cost re resources, time, people, rejection rate. R-2R Monolithic chips of old can be seen to be quite an achievement, in this light, especially the 'K' or 'S1, S2' variety.


Big J

"... only a very few individuals understand as yet that personal salvation is a contradiction in terms."


 

RE: Truncation of LSB's, posted on June 4, 2017 at 03:47:17
Todd Krieger
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 The LSB for 20-bit audio shuts off at -120 dB...... So unless the music itself is purely electronic in nature (and goes beyond 20 bits in depth), the four truncated bits are all acting deep in the noise floor........

Due to less RF switching, which generates less interference (provided the switching transistors require identical power), I'd even say that playing "24-bit audio" with a 20-bit DAC might be desirable, relative to using a 24-bit DAC.

This is all theory.... If you like what you hear, that's what matters most.

 

RE: Truncation of LSB's, posted on June 4, 2017 at 09:54:17
sideliner
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 Thank you for the explanation. While it does clarify a few things I still have some questions.

What prompted my curiosity is an article I read (linked bellow) that shows an 8-bit R-2R DAC that's basically comprised of 8 pairs of R/2R resistors - one pair representing each bit. Knowing that monolithic multibit chips such as the BB PCM1704 are basically laser trimmed resistors on a silicon chip, I simply wondered why can't the resistors on the chip be combined with outside discrete resistors to form a ladder network able to resolve a 24-bit word-depth signal.

Since my knowledge here is very limited, I know that I am probably oversimplifying things, so any light you can shed on this will be appreciated. As an example, why would BB put two 23-bit dacs to create the collinear architecture when an extra set of resistors (either as a single pair or multiple same-value paralleled pairs) would 'presumably' have worked. I know I'm missing something, hence my simplistic questions.

 

RE: Truncation of LSB's, posted on June 4, 2017 at 14:00:07
knewton
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Location: Mid-Atlantic/Northeast
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 First of all, I want to clearly state that I'm not a D/A architect. With that said, there are several reasons why an D/A designer might choose to utilize multiple smaller R-2R arrays rather than a single larger array. For one, multiple arrays enables moving the point of maximum glitching of the overall converter unit away from the waveform's zero crossing point, where it would otherwise be located with a single array. For another, you have to consider the primary obstacle to high resolution R-2R D/A unit design, which is the accuracy of the resistor elements (and the stability of that accuracy over changes in temperature and humidity).

For example, say you want to create a 20-bit single array R-2R converter unit. The dynamic range of such a converter is about 120dB, a ratio of roughly 1,000,000 : 1. Which means that the resistors in the array would need to have the same level of accuracy. In percentage terms, this is a 0.0001% tolerance. You can begin to see the technical challenges in producing a single accurate high resolution R-2R converter unit in a lab, let alone in commercial production. An D/A converter comprised of dual 19-bit arrays, however, can each utilize resistors of only twice the tolerance. The engineering and manufacturing problem isn't the number resistors needed as much as the very high accuracy required of them.

Under the no-free-lunch principle, multiple arrays would need to be tightly gain matched to each other, not to mention the additional control logic required to coordinate their operation. These issues rapidly gain complexity with the number of arrays being integrated.
_
Ken Newton

 

Yes, posted on June 5, 2017 at 22:47:46
Frihed89
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Location: Copenhagen
Joined: March 21, 2005
 And I think they built their own equipment to try to reach precision perfection. It hasn't been easy or cheap, I guess.

 

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